Boolean operations, joins, and the extended low hierarchy

Boolean Operations, Joins, and the Extended Low Hierarchy

We prove that the join of two sets may actually fall into a lower level of the extended low hierarchy [BBS86] than either of the sets. In particular, there exist sets that are not in the second level of the extended low hierarchy, EL2, yet their join is in EL2. That is, in terms of extended lowness, the join operator can lower complexity. Since in a strong intuitive sense the join does not lowe...

Web personalization using Extended Boolean Operations with Latent Semanti Indexing

The Boolean Hierarchy and the Polynomial Hierarchy: a Closer Connection

We show that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH3(k), where BH3(k) is the k th level of the Boolean hierarchy over Σ2 . This is an improvement over the known results [3], which show that the polynomial hierarchy would collapse to P [O(log . This result is significant in two ways. First, the theorem says that a deeper collapse of the Boole...

The Extended Low Hierarchy Is an In niteHierarchy 1

Balc azar, Book, and Sch oning introduced the extended low hierarchy based on the levels of the polynomial-time hierarchy as follows: for k 1, level k of the extended low hierarchy is the set ELP; k = fA j Pk (A) Pk 1(A SAT)g. Allender and Hemachandra and Long and Sheu introduced re nements of the extended low hierarchy based on the and -levels, respectively, of the polynomial-time hierarchy: ...

Locating P/poly Optimally in the Extended Low Hierarchy

The low hierarchy within NP and the extended low hierarchy h a ve turned out to be very useful in classifying many i n teresting language classes. We relocate P=poly from the third-level EL P 3 (Balcc azar et al., 1986) to the third-level EL P 3 of the extended low hierarchy. The location of P=poly in EL P 3 is optimal since, as shown by Allender and Hemachandra (1992), there exist sparse sets ...